Water Pistols and Children!

A while ago, I posted about some interesting problems posed in the Technology Review magazine.

  • Jerry Grossman has equipped n children with loaded water pistols and has them standing in an open field with no three of them in a straight line, such that the distances between pairs of them are distinct. At a given signal, each child shoots the closest other child with water. Show that if n is any even number, then it is possible (but not necessarily the case) that every child gets wet. Show that if n is odd, then necessarily at least one child stays dry.
  • Each of logicians A, B, and C wears a hat with a positive integer on it. The number on one hat is the sum of the numbers on the other two. The logicians take turns making statements, as follows:
    A: “I don’t know my number.”
    B: “My number is 15.”
    What numbers are on the hats of A and C?

I submitted my solutions (click here to read my submitted solutions) and lo and behold, one of the solutions got published in the latest Technology Review (click here)!


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